cdfglo {lmomco} | R Documentation

## Cumulative Distribution Function of the Generalized Logistic Distribution

### Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Logistic distribution given parameters (xi, α, and kappa) of the distribution computed by `parglo`. The cumulative distribution function of the distribution is

F(x) = 1/(1+e^{-y}) mbox{,}

where y is

y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{α}) mbox{ for } kappa ne 0 mbox{,and }

y = (x-xi)/α mbox{ for } kappa = 0 mbox{, and}

where F(x) is the nonexceedance probability for quantile x, xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.

### Usage

    cdfglo(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `parglo` or similar.

### Value

Nonexceedance probability (F) for x.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`quaglo`, `parglo`

### Examples

      lmr <- lmom.ub(c(123,34,4,654,37,78))
      cdfglo(50,parglo(lmr))

[Package lmomco version 0.92 Index]